125=2x⋅x

Rewrite the equation as 2x⋅x=125.

2x⋅x=125

Raise x to the power of 1.

2(x1x)=125

Raise x to the power of 1.

2(x1x1)=125

Use the power rule aman=am+n to combine exponents.

2×1+1=125

Add 1 and 1.

2×2=125

2×2=125

Divide each term in 2×2=125 by 2.

2×22=1252

Cancel the common factor of 2.

Cancel the common factor.

2×22=1252

Divide x2 by 1.

x2=1252

x2=1252

x2=1252

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x=±1252

Simplify the right side of the equation.

Rewrite 1252 as 1252.

x=±1252

Simplify the numerator.

Rewrite 125 as 52⋅5.

Factor 25 out of 125.

x=±25(5)2

Rewrite 25 as 52.

x=±52⋅52

x=±52⋅52

Pull terms out from under the radical.

x=±552

x=±552

Multiply 552 by 22.

x=±552⋅22

Combine and simplify the denominator.

Multiply 552 and 22.

x=±55222

Raise 2 to the power of 1.

x=±55222

Raise 2 to the power of 1.

x=±55222

Use the power rule aman=am+n to combine exponents.

x=±55221+1

Add 1 and 1.

x=±55222

Rewrite 22 as 2.

Use axn=axn to rewrite 2 as 212.

x=±552(212)2

Apply the power rule and multiply exponents, (am)n=amn.

x=±552212⋅2

Combine 12 and 2.

x=±552222

Cancel the common factor of 2.

Cancel the common factor.

x=±552222

Divide 1 by 1.

x=±5522

x=±5522

Evaluate the exponent.

x=±5522

x=±5522

x=±5522

Simplify the numerator.

Combine using the product rule for radicals.

x=±52⋅52

Multiply 2 by 5.

x=±5102

x=±5102

x=±5102

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

x=5102

Next, use the negative value of the ± to find the second solution.

x=-5102

The complete solution is the result of both the positive and negative portions of the solution.

x=5102,-5102

x=5102,-5102

x=5102,-5102

The result can be shown in multiple forms.

Exact Form:

x=5102,-5102

Decimal Form:

x=7.90569415…,-7.90569415…

Solve using the Square Root Property 125=2x*x